POST UTME IMS U 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let $a_n = \frac{1}{n^2}$ for $n = 1, 2, 3, \dots$. Find the sum of the series $\sum_{n=1}^\infty a_n$.
A. \frac{\pi^2}{6}
B. \frac{\pi^2}{12}
C. \frac{\pi^2}{24}
D. \frac{\pi^2}{36}
Question 2
A polynomial function $f(x)$ has the equation $f(x) = ax^3 + bx^2 + cx + d$. If the function has a root at $x = -2$, what is the value of $a$?
A. 2
B. -2
C. 4
D. -4
Question 3
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Solve the inequality $\frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0$.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -3 \) \cup \( -1, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup (1, 3)
Question 5
A quadratic equation $ax^2 + bx + c = 0$ has roots $x_1$ and $x_2$. If the sum of the roots is $-2$ and the product of the roots is $-3$, what is the value of $a$?
A. 1
B. 2
C. 3
D. 4
Question 6
Find the area of the triangle with vertices (0, 0), (2, 0), and (0, 3).
A. 3
B. 6
C. 9
D. 12
Question 7
Find the derivative of the function ( f(x) = \frac{x^2 - 4x + 3}{x^2 + 2x + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) - \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
B. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) + \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
C. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) - \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
D. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) + \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
Question 8
In the diagram below, find the value of x.
A. 4
B. 6
C. 8
D. 10
Question 9
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 10
A circle with center $C$ and radius $r$ has the equation $x^2 + y^2 = r^2$. If the point $P$ has coordinates $(x, y)$, what is the dis\tance from $P$ to the center $C$?
A. r
B. \sqrt{r^2}
C. r^2
D. 2r
Question 11
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -\\infty, -1 \) \\cup \( 3, \\infty \)
B. \( -\\infty, 1 \) \\cup \( 3, \\infty \)
C. \( -\\infty, -3 \) \\cup \( 1, \\infty \)
D. \( -\\infty, 3 \) \\cup \( 1, \\infty \)
Question 12
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 13
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 14
Solve for x in the equation \( \log_{2}\( x^2 \ \) = 4 ).
A. \( x = 16 \)
B. \( x = 8 \)
C. \( x = 4 \)
D. \( x = 2 \)
Question 15
A probability experiment has two indep\endent events $A$ and $B$. If the probability of event $A$ is $0.4$ and the probability of event $B$ is $0.6$, what is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8

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